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Abstract <p>We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9883_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \in (1,2)\)</EquationSource> <!--DANMath2460182Petrosyan-m1--> </InlineEquation> in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9883_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({{R}_{\delta }}\)</EquationSource> <!--DANMath2460182Petrosyan-m2--> </InlineEquation>-set.</p>

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Topological Structure of the Solution Set of a Cauchy Problem for Fractional Differential Inclusions with an Upper Semicontinuous Right-Hand Side

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  • 发表日期：

    2025年4月1日

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  • G. G. Petrosyan

摘要

Abstract

We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order \(\alpha \in (1,2)\) in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an \({{R}_{\delta }}\) -set.